Infection and transmission risks of COVID-19 in schools and their contribution to population infections in Germany: A retrospective observational study using nationwide and regional health and education agency notification data

Background School-level infection control measures in Germany during the early Coronavirus Disease 2019 (COVID-19) pandemic differed across the 16 federal states and lacked a dependable evidence base, with available evidence limited to regional data restricted to short phases of the pandemic. This study aimed to assess the (a) infection risks in students and staff; (b) transmission risks and routes in schools; (c) effects of school-level infection control measures on school and population infection dynamics; and (d) contribution of contacts in schools to population cases. Methods and findings For this retrospective observational study, we used German federal state (NUTS-2) and county (NUTS-3) data from public health and education agencies from March 2020 to April 2022. We assessed (a) infection risk as cumulative risk and crude risk ratios and (b) secondary attack rates (SARs) with 95% confidence interval (CI). We used (c) multiple regression analysis for the effects of infection control measures such as reduced attendance, mask mandates, and vaccination coverage as absolute reduction in case incidence per 100,000 inhabitants per 14 days and in percentage relative to the population, and (d) infection dynamic modelling to determine the percentage contribution of school contacts to population cases. We included (a) nationwide NUTS-2 data from calendar weeks (W) 46-50/2020 and W08/2021-W15/2022 with 3,521,964 cases in students and 329,283 in teachers; (b) NUTS-3 data from W09-25/2021 with 85,788 student and 9,427 teacher cases; and (c) detailed data from 5 NUTS-3 regions from W09/2020 to W27/2021 with 12,814 cases (39% male, 37% female; median age 14, range 5 to 63), 43,238 contacts and 4,165 secondary cases for students (for teachers, 14,801 [22% male, 50% female; median age 39, range 16 to 75], 5,893 and 472). Infection risk (a) for students and teachers was higher than the population risk in all phases of normal presence class and highest in the early 2022 omicron wave with 30.6% (95% CI 30.5% to 32.6%) of students and 32.7% (95% CI 32.6% to 32.8%) of teachers infected in Germany. SARs (b) for students and staff were below 5% in schools throughout the study period, while SARs in households more than doubled from 13.8% (95% CI 10.6% to 17.6%) W21-39/2020 to 28.7% (95% CI 27% to 30.4%) in W08-23/2021 for students and 10.9% (95% CI 7% to 16.5%) to 32.7% (95% CI 28.2% to 37.6%) for staff. Most contacts were reported for schools, yet most secondary cases originated in households. In schools, staff predominantly infected staff. Mandatory surgical mask wearing during class in all schools was associated with a reduction in the case incidence of students and teachers (c), by 56/100,000 persons per 14 days (students: 95% CI 47.7 to 63.4; teachers: 95% CI 39.6 to 71.6; p < 0.001) and by 29.8% (95% CI 25% to 35%, p < 0.001) and 24.3% (95% CI 13% to 36%, p < 0.001) relative to the population, respectively, as were reduced attendance and higher vaccination coverage. The contribution of contacts in schools to population cases (d) was 2% to 20%, lowest during school closures/vacation and peaked during normal presence class intervals, with the overall peak early during the omicron wave. Limitations include underdetection, misclassification of contacts, interviewer/interviewee dependence of contact-tracing, and lack of individual-level confounding factors in aggregate data regression analysis. Conclusion In this study, we observed that open schools under hygiene measures and testing strategies contributed up to 20% of population infections during the omicron wave early 2022, and as little as 2% during vacations/school closures; about a third of students and teachers were infected during the omicron wave in early 2022 in Germany. Mandatory mask wearing during class in all school types and reduced attendance models were associated with a reduced infection risk in schools.


Introduction
Background/rationale 2 Explain the scientific background and rationale for the investigation being reported Introduction Schools have been a key target domain for nonpharmaceutical interventions (NPIs) in the SARS-CoV-2 pandemic. However, infection dynamics in schools, their impact on the wider population and the effect of NPIs remain ill-defined.
In Germany and Europe, studies on school transmission risk and contribution to overall transmission in the population are based on geographically and temporally limited data Studies investigating school setting transmission in Germany are limited to small geographic units and short time periods.
In this study we obtained federal state and county level data for school settings as well as detailed regional data obtained from individual public health and educational agencies to assess infection risk, secondary attack rates, the contribution of schools to the overall transmission as well as the effect of NPIs in schools during the first 18 months of the pandemic in Germany.
Objectives 3 State specific objectives, including any prespecified hypotheses Introduction, S3 Text. 3.1 Aims In this study we obtained federal state and county level data for school settings as well as detailed regional data obtained from individual public health and educational agencies to assess infection risk, secondary attack rates, the contribution of schools to the overall transmission as well as the effect of NPIs in schools during the first 18 months of the pandemic in Germany.
The primary aim of this study is a better understanding of the risk of infection, the transmission of SARS-CoV-2 in schools, and the contribution of in-school contacts to overall cases in the population over different phases of the pandemic in Germany.
Moreover, we assess the reduction of risks of infection and transmission associated with specific measures taken in schools. Specific aims of the study are an analysis of the 1) risk of infection in students and staff in schools, 2) risk of notified infection for a contact person (secondary attack rate) of a notified student and staff index cases, and 3) effect of measures taken in schools to reduce the transmission of SARS-CoV-2. Whereas health and education agency data were used for Aims 1) and 2), data of the Standing Conference of Ministers of Education and Cultural Affairs in Germany (KMK) at NUTS-3 level was used for aim 3).

Study design 4
Present key elements of study design early in the paper Methodologystudy design and data sources we performed a retrospective observational study of prospectively collected SARS-CoV-2 infection case report data from health and educational authorities in Germany Setting 5 Describe the setting, locations, and relevant dates, including periods of recruitment, exposure, follow-up, and data collection Methodologystudy design and data sources, S1, S2, S3 Methodology: we used data collected by the Standing Conference of Ministers of Education and Cultural Affairs in Germany (KMK) (23). Federal state agencies collected data weekly in a structured format from all schools within their jurisdiction and included the number of students, classes and staff infected or absent due to quarantine and school closures. Federal state-level data is publicly available from calendar week (W) 46/2020 onwards, excluding school closures. In addition, we received unpublished countylevel data, collected in the same manner on the same parameters S1 We performed a descriptive analysis of infection risk for students and teachers as cumulative risks and crude risk ratios for specified periods of time with 95% Confidence Intervals (CI). We calculated secondary attack rates (SAR) as percentages with 95% CI of those being identified as notified infections in all known contacts.
We investigated infection control measures and other factors influencing infection risk of teachers or students in a multiple linear regression model. We used an ordinary least squares (OLS) model to test for statistical associations of the official active cases per 100000 students and teachers as reported by the KMK for the county level on the two-week-lags of the attendance rates (by educational level), the stringency of mask mandates (Table 1 in S3 Text) and the mandate and stringency of testing in schools. We controlled for the two-week incidence per 100000 inhabitants of the corresponding county, the percentage of fully vaccinated persons in the corresponding federal state, the socioeconomic status and geography of the county (S3 Text, S11 Text). Furthermore, we tested whether the school specific NPIs had an over proportional effect on the school population compared to the overall population. We proceeded similarly to the first approach, yet did not include a control group as an explanatory variable but instead divided the active cases among the students or teachers, respectively, by the 14-day incidence of the total population of the district. This way we estimated the effect of the NPIs on cases in schools relative to cases in the population, thus estimating whether the NPIs in schools have a significantly different effect on the overall population as on the school population.
The infection dynamics in schools were estimated using a SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) model previously described (27). This distinguishes between healthy but susceptible individuals, those infected but not yet infectious (exposed), and symptomatic and asymptomatic patients. In addition, we included compartments for hospitalisations, patients entering intensive care units (ICUs) and persons with long-COVID, i.e. those who continue to have sequelae after recovery.
In the final state, the patients are recovered or dead. Furthermore, we assume a reinfection process. We split the recovery compartment into a compartment for those recovered from COVID and a long-COVID compartment, since we assume that  We performed a retrospective observational study of prospectively collected SARS-CoV-2 infection case report data from health and educational authorities in Germany Public health authorities report case data according to the Infection Protection Act (IfSG). Cases were defined by direct viral detection via nasopharyngeal swabs using PCR or by cultural isolation of the pathogen.
S2 Table with information on regional agencies: R1, R3, R4, R5: All patients with detection of SARS-CoV-2 were contacted and interviewed by the local health department.

R2:
The condition for a case was the student or teacher self-reporting a positive SARS-CoV-2 PCR test to the school. The list of cases includes all infections reported by the school to the education authority.
Secondly, we used data collected by the Standing Conference of Ministers of Education and Cultural Affairs in Germany (KMK) (23). Federal state agencies collected data weekly in a structured format from all schools within their jurisdiction and included the number of students, classes and staff infected or absent due to quarantine and school closures.
Thirdly, we sourced population infection and incidence data from the Robert Koch Institute (RKI) SURVSTAT tool, described as incidence per 100000 inhabitants.

Bias 9
Describe any efforts to address potential sources of bias Methodology -Data analysis; Discussion; S12 Text. Additional

Limitations
We controlled for the two-week incidence per 100000 inhabitants of the corresponding county, the percentage of fully vaccinated persons in the corresponding federal state, the socioeconomic status and geography of the county (S3 Text, S11 Text). Furthermore, we tested whether the school specific NPIs had an over proportional effect on the school population compared to the overall population.

Data was analysed per calendar week (W) as the main time unit in
German state agency publications and avoids the weekly seasonality of data reporting (4) (no school on weekends, some local health agencies in Germany do not report data on weekends or Sunday).
We accounted for age-specific underdetection taking pandemic period-and age-specific underdetection ratios from a large seroprevalence study in Germany Limitations of our work are inherent in the notification process to both public health and educational agencies as well as the gathering of aggregate county-specific data (S12 Text). Both notification data itself as well as contact data is an underestimate of the actual infection dynamic. We attempted to account for underdetection with age-specific estimates taken from seroprevalence studies. This could make our estimate of contribution of school-contacts to overall transmission a potential underestimate. Residual confounding in the regression analysis is a possibility as we use aggregate county or school measures and did not have full access to individual-level confounding factors, e.g., on distribution of parental professions or industrial make-up of the counties included. We tried to include the most important confounding factors on infection dynamics in the population as well as deprivation and urbanity of counties in the analysis. SARs are limited by several factors. Contact tracing is inherently limited by both interviewer capacity and ability and interviewee memory and honesty, however with schools and households as contained domains the error margin is limited. Among contacts, the data did not indicate whether these were still susceptible to infection. However, it can be assumed that biases are similar in each region as they are situated within the same country and timeline of events. A reduction in the proportion of the susceptible population through vaccination or infection is assumed relevant from March 2021, where it is included as a parameter in regression analysis.
All considered, the SARs presented here described further transmission after cases have been detected in the school with limitations. S12 Text. Additional Limitations. Text not copied in due to excessive length Study size 10 Explain how the study size was arrived at Methodologystudy design and data sources; S2 Table We performed a retrospective observational study of prospectively collected SARS-CoV-2 infection case report data from health and educational authorities in Germany Public health authorities report case data according to the Infection Protection Act (IfSG). Cases were defined by direct viral detection via nasopharyngeal swabs using PCR or by cultural isolation of the pathogen.
All patients with detection of SARS-CoV-2 were contacted and interviewed by the local health department.
Federal state agencies collected data weekly in a structured format from all schools within their jurisdiction and included the number of students, classes and staff infected or absent due to quarantine and school closures.

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Quantitative variables 11 Explain how quantitative variables were handled in the analyses. If applicable, describe which groupings were chosen and why S3 Text. Additional Methodology; S11 Text.

Additional Results
Supplementary Results 3, Table 4 and 5 show previous analyses using the variable coding in Table 6. The original (full) model is presented next to the final model. The original selection of variables yielded some insensible and insignificant estimates due to multicollinearity (Table 7), thus some variables were excluded or rearranged for further analysis in the final model and the new variable grouping as per S3 Text, per 100000 students and teachers as reported by the KMK for the county level on the two-week-lags of the attendance rates (by educational level), the stringency of mask mandates (Table 1 in S3 Text) and the mandate and stringency of testing in schools. We controlled for the two-week incidence per 100000 inhabitants of the corresponding county, the percentage of fully vaccinated persons in the corresponding federal state, the socioeconomic status and geography of the county (S3 Text, S11 Text).
Furthermore, we tested whether the school specific NPIs had an over proportional effect on the school population compared to the overall population. We proceeded similarly to the first approach, yet did not include a control group as an explanatory variable but instead divided the active cases among the students or teachers, respectively, by the 14-day incidence of the total population of the district. This way we estimated the effect of the NPIs on cases in schools relative to cases in the population, thus estimating whether the NPIs in schools have a significantly different effect on the overall population as on the school population.
To control for the overall infection activity during that period, we downloaded weekly incidences per 100000 inhabitants for the districts for the total population of said districts (3). To account for socioeconomic effects, we used an index derived by Kroll (9).
The current values this index for the year 2015 were provided by Kroll (10). Moreover, we accounted for potential geographical effects of the districts, i.e. we may witness higher ceteris paribus (c.p.) infection risks for students who are living in highly rural areas and need to commute to school using public transports, which could increase their risk of infection. To test these effects on infection risks of students and teachers, we discriminated all districts according to the so-called RegioStar7 categorisation by the Federal Ministry of Transport and Digital Infrastructure, which defines 7 different categories of LAU regions (11).
The infection dynamics in schools were estimated using a SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) model previously described (27). This distinguishes between healthy but susceptible individuals, those infected but not yet infectious (exposed), and symptomatic and asymptomatic patients. In addition, we included compartments for hospitalisations, patients entering intensive care units (ICUs) and persons with long-COVID, i.e. those who continue to have sequelae after recovery.
In the final state, the patients are recovered or dead. Furthermore, we assume a reinfection process. We split the recovery compartment into a compartment for those recovered from COVID and a long-COVID compartment, since we assume that both have a different reinfection rate. The remaining parameters represent time periods of transitions between the different statuses as well as probabilities for the transitions and are estimated from international data and literature research. The data for the model is composed of reports from KMK (23), RKI (25) and the DIVI Intensive Care Register(28). We accounted for age-specific underdetection taking pandemic period-and age-specific underdetection ratios from a large seroprevalence study in Germany(29).
(b) Describe any methods used to examine subgroups and interactions Methodologydata analysis; Results; S1; S7; S8; S9; S10; S11 Text. Additional Results S1 Items included for analysis were the date of case notification, age of the index case, contacts and secondary cases (R1, R3-5), contact age (R1, R3, R5) and contact area (R1). Secondary attack rates (SARs) as percentages were calculated where possible.
Student and staff infection risk and incidences were calculated with school population data from regional or federal state authorities, analysed by age and school form as percentages where possible and described.
Results We accounted for age-specific underdetection taking pandemic period-and age-specific underdetection ratios from a large seroprevalence study in Germany (c) Explain how missing data were addressed Results; S1 Tables; S2 Tables Both notification data itself as well as contact data is an underestimate of the actual infection dynamic. We attempted to account for underdetection with age-specific estimates taken from seroprevalence studies. This could make our estimate of contribution of school-contacts to overall transmission a potential underestimate. Residual confounding in the regression analysis is a possibility as we use aggregate county or school measures and did not have full access to individual-level confounding factors, e.g., on distribution of parental professions or industrial make-up of the counties included. We tried to include the most important confounding factors on infection dynamics in the population as well as deprivation and urbanity of counties in the analysis. SARs are limited by several factors. Contact tracing is inherently limited by both interviewer capacity and ability and interviewee memory and honesty, however with schools and households as contained domains the error margin is limited. Among contacts, the data did not indicate whether these were still susceptible to infection.
However, it can be assumed that biases are similar in each region as they are situated within the same country and timeline of events. A reduction in the proportion of the susceptible population through vaccination or infection is assumed relevant from March 2021, where it is included as a parameter in regression analysis. All considered, the SARs presented here described further transmission after cases have been detected in the school with limitations.
S2 To control for the overall infection activity during that period, we downloaded weekly incidences per 100000 inhabitants for the districts for the total population of said districts (3). To account for socioeconomic effects, we used an index derived by Kroll (9).
The current values this index for the year 2015 were provided by Kroll (10). Moreover, we accounted for potential geographical effects of the districts, i.e. we may witness higher ceteris paribus (c.p.) infection risks for students who are living in highly rural areas and need to commute to school using public transports, which could increase their risk of infection. To test these effects on infection risks of students and teachers, we discriminated all districts according to the so-called RegioStar7 categorisation by the Federal Ministry of Transport and Digital Infrastructure, which defines 7 different categories of LAU regions (11).
(e) Describe any sensitivity analyses S11 Text Sensitivity Analysis S11 Text, Table 2 and 3 show the results of a sensitivity analysis splitting the observation period into rising infections during the 4th wave (W08-16) and waning infections during the 4th wave (W17-23). S11 Text, Table 4 and 5 show previous analyses using the variable coding in Table 6. The original (full) model is presented next to the final model. The original selection of variables yielded some insensible and insignificant estimates due to multicollinearity (Table 7), thus some variables were excluded or rearranged for further analysis in the final model and the new variable grouping as per S3 Text, Table 1.

Results
Participants 13* (a) Report numbers of individuals at each stage of study-eg numbers potentially eligible, examined for eligibility, confirmed eligible, included in the study, completing follow-up, and analysed S1 Limitations of our work are inherent in the notification process to both public health and educational agencies as well as the gathering of aggregate county-specific data (S12 Text). Both notification data itself as well as contact data is an underestimate of the actual infection dynamic. We attempted to account for underdetection with age-specific estimates taken from seroprevalence studies.

(c) Consider use of a flow diagram
Descriptive data 14* (a) Give characteristics of study participants (eg demographic, clinical, social) and information on exposures and potential confounders S1 Limitations to the data are inherent in the process of disease reporting and contact tracing. Underdetection of cases, especially in the younger age group, will affect infection risk. Regional differences in infection environment and NPI adherence affect infection risk and make inter-regional comparison difficult. NPIs affecting domains of life other than schools were not considered and differed by federal state in Germany. R1, R2 and R4 collated data on students separately, with a margin of error in picking up the relevant classification of cases from contact tracing. R3 and R5 identified students based on age, thus older (in particular vocational) students will not be perfectly reflected in the analysis. Furthermore, health agencies collate cases based on registered place of residence. In particular R4 data will be affected by crossborder (country and county) commuters and administrative differentiation of cases by residence, as would be R1, R2 and R5 through peri-urban commuting. Contact tracing fidelity depends on capacity and capability of health agencies, reporting by index cases and is inherently flawed. This is obvious in that a) the reproduction numbers for regions where full population datasets were provided (R3, R5) is below 1 and thus not compatible with the pandemic progression witnessed and b) on average, only 65% of index cases had any contacts reported at all (R1 54%, R3 54%, R4 42% and R5 84%), leading to a skewed picture of contacts and secondary attack rates as well as biases as to which index cases would have reported contacts and how or whether they would have been identified as secondary cases by authorities in due course. Furthermore, especially for household cases the direction of transmission in instances of multiple household cases cannot always be clearly ascertained, the same holds true for attribution of origin of infected to any one contact, particularly during phases of high transmission.
S9 Tables gives the number of cases with contacts reported. It is not known whether these were cases without contacts, without a detailed contact tracing or whether the index case did not report contacts.
The ordinary least squares (OLS) model for the official active cases per 100000 students and teachers as reported by the KMK showed that in counties with a mask mandate during class in all types of schools (i.e. primary schools as well as secondary schools) the average number of weekly cases was lower by 56 per 100000 cases for both the students and teachers (Table 3). The mandate was associated with a greater reduction of infection activity among students and teachers than the total population.
The mask mandate in class for all types of schools was associated with a reduction of case numbers relative to the general population of 29.8% for students and 24.3% for teachers (S11 Text, Table 1). Mandatory testing in schools in our study period was associated with an average increase of 50 notifications per 100000 per 14 days among students. (Table 2, S11 Text).
Urban counties were associated with a higher number of notified infections in students and a lower number in teachers compared to rural counties (S11 Text). A high degree of social deprivation in a county was associated with higher numbers of infections in teacher (S11 Text). Not accounting for underestimation of infections, we found a high variability in the contribution of contacts from school infections to the overall transmission during the third wave from 2-12%. Accounting for age-specific underestimation of notified infections in comparison to actual infections based on seroprevalence estimates, this range was 2-13% (Fig.6).
(b) Report category boundaries when continuous variables were categorized S11 Text S11 Text, Table 4 and 5 show previous analyses using the variable coding in Other analyses 17 Report other analyses done-eg analyses of subgroups and interactions, and sensitivity analyses S8 Text S9 Text S11 Text e.g. S11 Text: Sensitivity Analysis S11 Text, Table 2 and 3 show the results of a sensitivity analysis splitting the observation period into rising infections during the 4th wave (W08-16) and waning infections during the 4th wave (W17-23). S11 Text, Table 4 and 5 show previous analyses using the variable coding in Table 6. The original (full) model is presented next to the final model. The original selection of variables yielded some insensible and insignificant estimates due to multicollinearity (Table 7), thus some variables were excluded or rearranged for further analysis in the final model and the new variable grouping as per S3 Text, Table 1.

Discussion
Key results 18 Summarise key results with reference to study objectives Discussion In this study of infection and transmission risks during the pandemic in Germany, we could show that the contribution of infection dynamics in schools to that of the general population was up to 13% under hygiene and testing measures. Furthermore, NPIs such as strict mask mandates (in all schools during class) and reduced presence models are associated with an effective reduction in infection and transmission risks in schools and their contribution to population infections.
We estimate a reduction by 24-30% of infection risk for both students and teachers relative to the population and by more than 55/100.000 per 14 days in absolute case numbers in those counties implementing mandatory surgical mask wearing during class in all schools.
These findings are reflected in our analysis on the contribution of schools to the general population infection dynamics. School vacation and closures reduced this contribution to as low as 2%. The peak at 12% contribution in W24 occurs with open schools, loosening population NPIs and loosening but still strict hygiene and testing measures in schools.
Meanwhile, the lower peak at 7% early in phase 4 occurred during reduced attendance class models and stricter NPIs.
The majority of secondary cases of both students and staff happened in households. In schools, age-specific SARs show that transmission took place mostly from staff to staff and from student to student more than student to staff.
Most infections and transmission in school took place in phase 3a when schools operated in normal class models with some cloth mask rules and general hygiene concepts. Teachers showed a higher risk of infection than the general population. Infection risk for students increased with age.
Limitations 19 Discuss limitations of the study, taking into account sources of potential bias or imprecision. Discuss both direction and magnitude of any potential bias Discussion S12 Text Limitations of our work are inherent in the notification process to both public health and educational agencies as well as the gathering of aggregate county-specific data (S12 Text). Both notification data itself as well as contact data is an underestimate of the actual infection dynamic. We attempted to account for underdetection with age-specific estimates taken from seroprevalence studies. This could make our estimate of contribution of school-contacts to overall transmission a potential underestimate. Residual confounding in the regression analysis is a possibility as we use aggregate county or school measures and did not have full access to individual-level confounding factors, e.g., on distribution of parental professions or industrial make-up of the counties included. We tried to include the most important confounding factors on infection dynamics in the population as well as deprivation and urbanity of counties in the analysis. SARs are limited by several factors. Contact tracing is inherently limited by both interviewer capacity and ability and interviewee memory and honesty, however with schools and households as contained domains the error margin is limited. Among contacts, the data did not indicate whether these were still susceptible to infection. However, it can be assumed that biases are similar in each region as they are situated within the same country and timeline of events. A reduction in the proportion of the susceptible population through vaccination or infection is assumed relevant from March 2021, where it is included as a parameter in regression analysis. All considered, the SARs presented here described further transmission after cases have been detected in the school with limitations.
Limitations to the data are inherent in the process of disease reporting and contact tracing. Underdetection of cases, especially in the younger age group, will affect infection risk. Regional differences in infection environment and NPI adherence affect infection risk and make interregional comparison difficult. NPIs affecting domains of life other than schools were not considered and differed by federal state in Germany. R1, R2 and R4 collated data on students separately, with a margin of error in picking up the relevant classification of cases from contact tracing. R3 and R5 identified students based on age, thus older (in particular vocational) students will not be perfectly reflected in the analysis. Furthermore, health agencies collate cases based on registered place of residence. In particular R4 data will be affected by cross-border (country and county) commuters and administrative differentiation of cases by residence, as would be R1, R2 and R5 through peri-urban commuting.
Contact tracing fidelity depends on capacity and capability of health agencies, reporting by index cases and is inherently flawed. This is obvious in that a) the reproduction numbers for regions where full population datasets were provided (R3, R5) is below 1 and thus not compatible with the pandemic progression witnessed and b) on average, only 65% of index cases had any contacts reported at all (R1 54%, R3 54%, R4 42% and R5 84%), leading to a skewed picture of contacts and secondary attack rates as well as biases as to which index cases would have reported contacts and how or whether they would have been identified as secondary cases by authorities in due course. Furthermore, especially for household cases the direction of transmission in instances of multiple household cases cannot always be clearly ascertained, the same holds true for attribution of origin of infected to any one contact, particularly during phases of high transmission. Among contacts, it was not possible to ascertain from the data whether these were still susceptible to infection. However, it can be assumed that biases are similar in each region as they are situated within the same state and timeline of events, and that a reduction in the proportion of the susceptible population through vaccination or infection is assumed relevant from March 2021, where it is included as a parameter in regression analysis. All considered, the SAR parameter describes further transmission after cases have been detected in the school with limitations.
Compared to health agencies, education agencies are not trained in contact tracing and systematic disease reporting, thus a greater margin of error is to be expected in those datasets gathered by education authorities.
A thorough interpretation of our results has to take into account significant limitations associated with our data. The regressions based on the KMK data span only a relatively narrow time window, which spans from calendar week 8-25 of 2021. Therefore, there may be time effects, which should be considered but cannot be included sufficiently in a statistical analysis. We tried to control for this to some extent by including the overall infection level in the local populace. Moreover, our intervention variables are obviously not ideal but rather a collection of either binary variables or approximations to include the differences in stringency of measures and attendance in school and roughly quantify the impacts these measures have on the infection risks of students and teachers as best as possible with limited data. As the NPIs have been introduced as bundles in most cases, we do not have a perfect experimental environment that would be needed for an optimal assessment of the NPIs' impacts on the infection risks. Therefore, the coefficients could be slightly biased in some cases as the Gauß-Markov assumptions, especially independence among the explanatory variables, are not completely fulfilled. We chose the variables in a manner that multicollinearity is minimised as well as possible, yet perfect independence is not given in the data. Another major limitation is the lack of comparability between the KMK and the RKI data. Whereas the RKI reports new cases weekly which can be stratified by age groups, the KMK reports known and current sick cases due to COVID-19. We tried to circumvent this limitation by comparing new cases of the previous two calendar weeks, as reported by the RKI, to the sick numbers reported by the KMK. The assumption behind this is that students or teachers currently excused from school due to an infection have been infected in one of the previous two weeks, which appears a reasonable assumption given the incubation time (13). Furthermore, KMK data do not discriminate by type of school on the district level and demographic data on the students and teachers is not reported. Finally, the KMK data may be vulnerable towards higher underdetection of COVID-19 cases, as students and teachers are not obligated to report their reason of absence correctly, i.e. it is not ensured that someone being excused from school will indeed report the real reason for their absence.
Interpretation 20 Give a cautious overall interpretation of results considering objectives, limitations, multiplicity of analyses, results from similar studies, and other relevant evidence Discussion Despite these limitations we conclude that school setting contribution to overall transmission in the population is relevant, but variable over different time periods in the pandemic and responsive to NPIs. In Germany, school-related NPIs, in particular masking and reduced attendance, have been successful in mitigating the spread of the virus among both students and teachers.
Generalisability 21 Discuss the generalisability (external validity) of the study results Discussion S12 Text A thorough interpretation of our results has to take into account significant limitations associated with our data. The regressions based on the KMK data span only a relatively narrow time window, which spans from calendar week 8-25 of 2021. Therefore, there may be time effects, which should be considered but cannot be included sufficiently in a statistical analysis. We tried to control for this to some extent by including the overall infection level in the local populace. Moreover, our intervention variables are obviously not ideal but rather a collection of either binary variables or approximations to include the differences in stringency of measures and attendance in school and roughly quantify the impacts these measures have on the infection risks of students and teachers as best as possible with limited data. As the NPIs have been introduced as bundles in most cases, we do not have a perfect experimental environment that would be needed for an optimal assessment of the NPIs' impacts on the infection risks.
Contact tracing fidelity depends on capacity and capability of health agencies, reporting by index cases and is inherently flawed. This is obvious in that a) the reproduction numbers for regions where full population datasets were provided (R3, R5) is below 1 and thus not compatible with the pandemic progression witnessed and b) on average, only 65% of index cases had any contacts reported at all (R1 54%, R3 54%, R4 42% and R5 84%), leading to a skewed picture of contacts and secondary attack rates as well as biases as to which index cases would have reported contacts and how or whether they would have been identified as secondary cases by authorities in due course. Furthermore, especially for household cases the direction of transmission in instances of multiple household cases cannot always be clearly ascertained, the same holds true for attribution of origin of infected to any one contact, particularly during phases of high transmission.